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On the class number of certain cyclotomic fields
Abstract
We construct four infinite families of cyclotomic fields and show that each member of these families has class number a multiple of 3. In fact, we show that the class number of the corresponding maximal real subfields has class number divisible by 3. A construction by Kishi and Miyake [11] and a result of Yamaguchi [13] help us achieve this target. Finally, we produce computational evidence corroborating our results.
Related
- Ideal class groups of certain real quadratic number fields and factorizations of values of certain quadratic polynomials
- Density of Vanishing of Certain Eigenspaces of Cyclotomic Class Groups
- Post-critically finite polynomials over cyclotomic closures of number fields
- p-class groups in the cyclotomic ℤp-extension of imaginary quadratic fields
- Monogenicity and 2-torsion in the class group of number fields of odd degree
BibTeX
@misc{chakraborty2026class,
title = {{On the class number of certain cyclotomic fields}},
author = {Kalyan Chakraborty and Pratik Rao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05950},
eprint = {2609.05950},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05950},
}
RIS
TY - UNPB
TI - On the class number of certain cyclotomic fields
AU - Kalyan Chakraborty
AU - Pratik Rao
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05950
UR - https://arxiv.org/abs/2609.05950
AB - We construct four infinite families of cyclotomic fields and show that each member of these families has class number a multiple of 3. In fact, we show that the class number of the corresponding maximal real subfields has class number divisible by 3. A construction by Kishi and Miyake [11] and a result of Yamaguchi [13] help us achieve this target. Finally, we produce computational evidence corroborating our results.
ER -